A machine gun is mounted on a 2000kg car on a horizontal frictionless surface. At some instant the gun fires bullets of mass 10gm with a velocity of `500 m//sec` with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is

Options

A. 550N
B. 50N
C. 250N
D. 250N dyne

Explanation

To solve the problem, we need to calculate the average thrust exerted by the machine gun mounted on the car. The thrust can be calculated using the formula:

\[ \text{Thrust} = V \cdot \frac{dm}{dt} \]

where:
- \( V \) is the velocity of the bullets with respect to the car,
- \( \frac{dm}{dt} \) is the rate of change of mass, which represents the mass flow rate of the bullets.

### Step 1: Identify the values given in the problem
- Mass of one bullet, \( m = 10 \, \text{g} = 10 \times 10^{-3} \, \text{kg} \)
- Velocity of the bullet, \( V = 500 \, \text{m/s} \)
- Number of bullets fired per second, \( n = 10 \, \text{bullets/s} \)

### Step 2: Calculate the rate of change of mass \( \frac{dm}{dt} \)
The rate of change of mass can be calculated as:

\[ \frac{dm}{dt} = \text{mass of one bullet} \times \text{number of bullets fired per second} \]

Substituting the values:

\[ \frac{dm}{dt} = (10 \times 10^{-3} \, \text{kg}) \times (10 \, \text{bullets/s}) = 10 \times 10^{-2} \, \text{kg/s} = 0.1 \, \text{kg/s} \]

### Step 3: Substitute \( V \) and \( \frac{dm}{dt} \) into the thrust formula
Now, we can substitute the values into the thrust formula:

\[ \text{Thrust} = V \cdot \frac{dm}{dt} = 500 \, \text{m/s} \cdot 0.1 \, \text{kg/s} \]

### Step 4: Calculate the thrust
Calculating the thrust gives:

\[ \text{Thrust} = 500 \cdot 0.1 = 50 \, \text{N} \]

### Conclusion
The average thrust on the system is \( 50 \, \text{N} \).

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